Space of modular forms of level 3234, weight 2, and Character 3234.bw

• Label: 3234.2.bw
• Level: $3234$
• Weight: $2$
• Character orbit: 3234.bw
• Rep. character: $\chi_{3234}(89,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $2256$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.bw (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 147 \)
Character field:			\(\Q(\zeta_{42})\)
Sturm bound:			\(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3234, [\chi])\).

	Total	New	Old
Modular forms	8160	2256	5904
Cusp forms	7968	2256	5712
Eisenstein series	192	0	192

Trace form

2256 * q - 188 * q^4 - 28 * q^6 - 16 * q^7 - 32 * q^9 + 24 * q^15 + 188 * q^16 + 24 * q^19 - 16 * q^21 + 12 * q^24 + 196 * q^25 - 8 * q^28 - 8 * q^30 - 24 * q^31 + 20 * q^36 + 68 * q^37 + 12 * q^39 + 48 * q^42 - 16 * q^43 - 48 * q^45 + 312 * q^46 + 40 * q^49 + 12 * q^51 - 32 * q^52 + 36 * q^54 + 60 * q^57 + 52 * q^58 + 12 * q^60 - 112 * q^61 + 56 * q^63 + 376 * q^64 + 8 * q^67 - 32 * q^70 - 48 * q^73 - 132 * q^75 + 32 * q^81 - 24 * q^82 - 80 * q^84 - 128 * q^85 + 36 * q^87 - 84 * q^90 + 16 * q^91 + 536 * q^93 + 48 * q^94 + 12 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(3234, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3234, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1617, [\chi])\)\(^{\oplus 2}\)